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Various numbers play a significant role in Jewish texts or practice. Some such numbers were used as mnemonics to help remember concepts, while other numbers were considered to have intrinsic significance or allusive meaning. Numbers such as 7, 10, 12, and 40 were known for recurring in symbolic contexts.
Dov Jarden gave a simple non-constructive proof that there exist two irrational numbers a and b, such that a b is rational: [28] [29] Consider √ 2 √ 2; if this is rational, then take a = b = √ 2. Otherwise, take a to be the irrational number √ 2 √ 2 and b = √ 2. Then a b = (√ 2 √ 2) √ 2 = √ 2 √ 2 · √ 2 = √ 2 2 = 2 ...
11 is a prime number, and a super-prime. 11 forms a twin prime with 13, [6] and sexy pair with 5 and 17. 11 is also the first prime exponent that does not yield a Mersenne prime. 11 is also a Gaussian prime [7] and an Eisenstein prime. [8] 11 is part of a pair of Brown numbers. Only three such pairs of numbers are known.
The real number x is a rational number only if its decimal expansion is eventually periodic, that is if there are natural numbers N and p such that for every n ≥ N it is the case that a n+p = a n. Another way of expressing numbers is to write them as simple continued fractions, as in:
The system of Hebrew numerals is a quasi-decimal alphabetic numeral system using the letters of the Hebrew alphabet.The system was adapted from that of the Greek numerals sometime between 200 and 78 BCE, the latter being the date of the earliest archeological evidence.
The following 1953 proof by Dov Jarden has been widely used as an example of a non-constructive proof since at least 1970: [4] [5] CURIOSA 339. A Simple Proof That a Power of an Irrational Number to an Irrational Exponent May Be Rational. is either rational or irrational. If it is rational, our statement is proved.
Postmodern Jewish philosophy narratives of meaning [23] Independent scholarship: Sanford Drob – The New Kabbalah [24] Zevi Slavin – Seekers of Unity [25] Zionist and monistic mystical thought of Rav Kook: c. 1910s–today: Innovative teachings and influence of Abraham Isaac Kook, pre-State Chief Rabbi of Mandate Palestine and poetic mystic.
In mathematics, an irrational number is any real number that is not a rational number, i.e., one that cannot be written as a fraction a / b with a and b integers and b not zero. This is also known as being incommensurable, or without common measure. The irrational numbers are precisely those numbers whose expansion in any given base (decimal ...